Question

The perimeter of a rectangle is 40 centimetres and its area is 96 square centimetres .

a) What is the sum of the lengths of the longer and the shorter sides of the rectangle ?

b)Write down a second degree equation by taking the length of the longer side as 10 + x

c) What are the lengths of its the sides ?​

Answer 1

Answer:

a) 20 cm

b) x² + 10x - 96 = 0

c) Length = 12 cm and Breadth = 8 cm

Step-by-step explanation:

Given,

Perimeter, P = 40 cm

Area, A = 96 cm²

We Know That,

Perimeter of rectangle = 2(L + B)

Perimeter of rectangle = 2(L + B)Area of rectangle = L * B

=> P = 2(l + b) = 40

=> l + b = 20 ---------(1)

=> A = l * b = 96 --------(2)

[ From (1) & (2), by using Trial and Error method

We will get Length = 12 & Breadth = 8 ]

Therefore, Length = 12 cm & Breadth = 8 cm

(a) Length of longer side + Shorter side

==> L + B = 12 + 8 = 20 cm

(b) Equation

Length = 10 + x

Area = l*b = 96

==> x(10 + x) = 96

==> 10x + x² = 96

==> x² + 10x - 96 = 0

(c) Length = 12 cm and Breadth = 8 cm

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Answer 2

Answer:

1] The sum of the lengths of the longer and the shorter sides of the rectangle is 20 cm

2]

${x}^{2} + 10x - 96 = 0$

3] the lengths of its the sides are 8cm and 12cm

Step-by-step explanation:

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